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   "metadata": {},
   "source": [
    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Given sorted arrays A, B, merge B into A in sorted order.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Does A have enough space for B?\n",
    "    * Yes\n",
    "* Can the inputs have duplicate array items?\n",
    "    * Yes\n",
    "* Can we assume the inputs are valid?\n",
    "    * No\n",
    "* Does the inputs also include the actual size of A and B?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* A or B is None -> Exception\n",
    "* index of last A or B < 0 -> Exception\n",
    "* A or B is empty\n",
    "* General case\n",
    "    * A = [1,  3,  5,  7,  9,  None,  None,  None]\n",
    "    * B = [4,  5,  6]\n",
    "    * A = [1, 3, 4, 5, 5, 6, 7, 9]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "<pre>\n",
    "                     i                 k\n",
    "A = [1,  3,  5,  7,  9,  None,  None,  None]\n",
    "             j\n",
    "B = [4,  5,  6]\n",
    "\n",
    "---\n",
    "\n",
    "A[k] = max(A[i], B[j])\n",
    "                     i                 k\n",
    "A = [1,  3,  5,  7,  9,  None,  None,  9]\n",
    "             j\n",
    "B = [4,  5,  6]\n",
    "\n",
    "---\n",
    "\n",
    "A[k] = max(A[i], B[j])\n",
    "                 i              k       \n",
    "A = [1,  3,  5,  7,  9,  None,  7,  9]\n",
    "             j\n",
    "B = [4,  5,  6]\n",
    "\n",
    "---\n",
    "\n",
    "A[k] = max(A[i], B[j])\n",
    "             i           k              \n",
    "A = [1,  3,  5,  7,  9,  6,  7,  9]\n",
    "             j\n",
    "B = [4,  5,  6]\n",
    "\n",
    "---\n",
    "\n",
    "A[k] = max(A[i], B[j])\n",
    "             i       k                  \n",
    "A = [1,  3,  5,  7,  5,  6,  7,  9]\n",
    "         j    \n",
    "B = [4,  5,  6]\n",
    "\n",
    "---\n",
    "\n",
    "A[k] = max(A[i], B[j])\n",
    "         i       k                      \n",
    "A = [1,  3,  5,  5,  5,  6,  7,  9]\n",
    "         j    \n",
    "B = [4,  5,  6]\n",
    "\n",
    "---\n",
    "\n",
    "A[k] = max(A[i], B[j])\n",
    "         i   k                          \n",
    "A = [1,  3,  4,  5,  5,  6,  7,  9]\n",
    "     j        \n",
    "B = [4,  5,  6]\n",
    "\n",
    "---\n",
    "\n",
    "A[k] = max(A[i], B[j])\n",
    "        ik                              \n",
    "A = [1,  3,  4,  5,  5,  6,  7,  9]\n",
    "             \n",
    "B = [4,  5,  6]\n",
    "\n",
    "---\n",
    "\n",
    "A = [1, 3, 4, 5, 5, 6, 7, 9]\n",
    "\n",
    "</pre>\n",
    "\n",
    "Complexity:\n",
    "* Time: O(m + n)\n",
    "* Space: O(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Array(object):\n",
    "\n",
    "    def merge_into(self, source, dest, source_end_index, dest_end_index):\n",
    "        if source is None or dest is None:\n",
    "            raise TypeError('source or dest cannot be None')\n",
    "        if source_end_index < 0 or dest_end_index < 0:\n",
    "            raise ValueError('end indices must be >= 0')\n",
    "        if not source:\n",
    "            return dest\n",
    "        if not dest:\n",
    "            return source\n",
    "        source_index = source_end_index - 1\n",
    "        dest_index = dest_end_index - 1\n",
    "        insert_index = source_end_index + dest_end_index - 1\n",
    "        while dest_index >= 0:\n",
    "            if source[source_index] > dest[dest_index]:\n",
    "                source[insert_index] = source[source_index]\n",
    "                source_index -= 1\n",
    "            else:\n",
    "                source[insert_index] = dest[dest_index]\n",
    "                dest_index -= 1\n",
    "            insert_index -= 1\n",
    "        return source"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_merge_into.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_merge_into.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestArray(object):\n",
    "\n",
    "    def test_merge_into(self):\n",
    "        array = Array()\n",
    "        assert_raises(TypeError, array.merge_into, None, None, None, None)\n",
    "        assert_raises(ValueError, array.merge_into, [1], [2], -1, -1)\n",
    "        a = [1, 2, 3]\n",
    "        assert_equal(array.merge_into(a, [], len(a), 0), [1, 2, 3])\n",
    "        a = [1, 2, 3]\n",
    "        assert_equal(array.merge_into(a, [], len(a), 0), [1, 2, 3])\n",
    "        a = [1,  3,  5,  7,  9,  None,  None,  None]\n",
    "        b = [4,  5,  6]\n",
    "        expected = [1, 3, 4, 5, 5, 6, 7, 9]\n",
    "        assert_equal(array.merge_into(a, b, 5, len(b)), expected)\n",
    "        print('Success: test_merge_into')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestArray()\n",
    "    test.test_merge_into()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_merge_into\n"
     ]
    }
   ],
   "source": [
    "%run -i test_merge_into.py"
   ]
  }
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